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stbenge wrote:
> Which I do.
Me too.
> That's not _all_ we can do ;) Dreams, for instance, can facilitate new
> learning experiences. But that's not the end of the possibilities. Some
> are more morally accepted than others, though.
I agree.
> Which, based on my experiences of this life, I can only guess that we'll
> have as much fun and as much good company as this one :)
I really hope so :)
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Saul Luizaga <sau### [at] netscape net> wrote:
> I find it to be the most frustrating and fascinating thing ever. I did a
> search for its objects:
Yes, me too. Fascinating because I have a kind of feeling that it's sort of
real; frustrating, because I can't imagine it.
Over the past months I've read some stuff about it. But sometimes only part of
the books, because I often didn't succeed in understanding the examples (I have
a very bad understanding of all mathemetical related things), let alone
imagining it.
There are many interesting resources on the topic. I assume you already know the
Pov-Ray generated films:
http://www.dimensions-math.org/Dim_E.htm
I found them very intriguing, though too difficult to understand sometimes.
Apart from the classic novel Flatland there seem to have been written quite a
lot of books and essays on the topic between 1880 and about 1925, maybe because
the topic was inspiring to those day's broader interest in mysticism and
theosophy, e.g. Ouspensky's Tertium Organum and some essays by Rudolf Steiner.
I thought the books by "amateur-mathematician" Charles Howard Hinton most
interesting, because I got the impression that he really was capable of imagine
a little of the 4th dimension, at least in so far as it can be imagined.
Some of his books can be downloaded for free, e.g.:
http://www.archive.org/details/fourthdimension00hintarch
He developed a set of coloured cubes (that could be bought along with his books
at that time) which were supposed to facilitate the imagination of the hypercube
in his book "The fourth dimension":
http://www.greylodge.org/occultreview/glor_011/hintoncubes.pdf
I haven't tried yet to make these models, because I was too lazy and thought
maybe it wouldn't help and I would possibly be more frustrated than before. When
reading through part of "The fourth dimension" I noticed however, that there
would be no chance to understand it properly without models. I also thought of
recreating them in POV too, but it seems to be an awful lot of work.
However Hinton's approach to visualizing the 4th dimension is supposed to have
had a strong influence on Alicia Boole Stott, too, who herself had no formal
education in mathematics either but managed to get a honorary doctorate in 1914
because of her work on four dimensional polytopes. She made lots of beautiful
cardboard models and one gets the impression that she too was capable of
"imagining" at least some sort of 4th dimension.
Regards,
Simone
> http://search.viewpoint.com/pl/websearch?vb=2&tn=&type=ONE&k=4th+dimension+objects
>
> I don't know if some day would be possible but would be great to visit a
> 4D world and meet 4D people :-D
>
> I was thinking and maybe this is where you go when you die and ghosts
> are just what we can see from a 4D person. 4D makes my head go thinking
> pretty bizarre stuff, don't you?
>
> Cheers.
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Interesting... yes I downloaded the movie but haven't seen it yet, yes I
have trouble also imagining 4D object, I think reading the 4D Cartesian
coordinate system and basic elements like a "line" and a "plane" could
help imagining more complex forms, thanks for the tips, I'll check them
out later.
Cheers.
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stbenge wrote:
> It's good to know that some people are taking the idea of a fourth
> spatial dimension seriously. A lot of people argue that time is the
> "true" 4th dimension, but that idea just doesn't sit well with me, even
> though I don't have a lot of knowledge in this area.
An extra spatial dimension gives you 4D Euclidian space.
Time as an extra dimension gives you a 4D non-Euclidian space, which
turns out to be useful in Einstien's various reletivity theories.
These are two seperate, unrelated geometries.
4D Euclidian space is interesting because it's a straight extension of
3D Euclidian geometry.
And then, as I mentioned, there are other non-Euclidian geometries. For
example, elliptic geometry. In 2D elliptic geometry, a "straight line"
is in fact a line drawn on the surface of a sphere. Since the surface of
a sphere is curved, all these "straight lines" curve around it and
eventually close into circles. (E.g., the Earth's equator is such a
circle.) Thus, in elliptic geometry, *all* lines intersect each other,
and there is no such thing as "parallel" lines.
Somewhat weirder is hyperbolic geometry, where multiple "straight lines"
through a single point do not intersect each other [except at that
point]. You really need to play with this:
http://cs.unm.edu/~joel/NonEuclid/NonEuclid.html
I lost hours in it...
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stbenge schrieb:
> It's good to know that some people are taking the idea of a fourth
> spatial dimension seriously. A lot of people argue that time is the
> "true" 4th dimension, but that idea just doesn't sit well with me, even
> though I don't have a lot of knowledge in this area.
Just one stupid question: What is there to be taken serious about - I
mean, if not considering time to be the 4th dimension (which it actually
is)?
The main point is that /if/ such a 4th ("space-like") dimension /does/
exist, then our 3 dimensions /already are/ embedded in that 4D world -
the 4th dimension will not just suddenly appear out of thin air to
entertain us.
There is no room for "serious" speculation about "what would it be like
if there /was/ a 4th dimension" - either a 4th (space-like) dimension
/does/ exist, in which case the natural laws in this 4D world /must/
result in the effects we observe in "our" 3D "slice" - or such a 4th
dimension does /not/ exist, in which case there's no room for
speculation left.
In any case we cannot in any way "leave 3D and enter 4D" - all we can do
is act within our 3D world, and (possibly) find that the resulting
effects can only (or best) be explained by assuming that our 3D world is
just a "slice" embedded in a 4D world.
Scientists are, by the way, seriously discussing models according to
which the universe does indeed have more than three space-like
dimensions (quite a lot actually), but they appear to agree that in this
case those extra dimensions must be quite small (think of the surface of
a thin wire, with the length corresponding to our known three space-like
dimensions, and the circumfence corresponding to the extra dimensions).
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Kevin Wampler schrieb:
> It is worth nothing, however, that the time dimension is *not* identical
> to the space dimensions (one would hope not!) and distances are measured
> differently in time than in space.
Well, AFAIK there's actually no fundamental reason to apply different
"measuring tapes" to time and space: The constant vacuum speed of light
can serve as a ruler for both, with the distance of a light second
equating a second.
It just happens that it's still more practical to use meters for
space-like dimensions and seconds for time-like dimensions.
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Saul Luizaga schrieb:
>>> Or maybe you leave your 3D body and become a 4D spirit that then will
>>> incarnate a 4D being and so on...
>>
>> But if so, how could you possible remember and/or integrate the
>> experience with a 3D mind? Maybe you could remember that *something*
>> happened, with a gained benefit of a new spiritual perspective...
>
> Is a possibility, but again, who remembers being a 2D person before this
> life? maybe is part of the "instinct" of each person, but who knows...
You can't be (and never could have been in any prior life) a "2D
person": Evidently, there /are/ 3 dimensions (or more), so each "2D"
being must also be embedded in 3D space, and therefore /be/ a 3D being.
Similarly with 4 (space-like) dimensions: Either we /are/ 4D beings, or
there is no such thing as a 4th dimension.
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>> It is worth nothing, however, that the time dimension is *not*
>> identical to the space dimensions (one would hope not!) and distances
>> are measured differently in time than in space.
>
> Well, AFAIK there's actually no fundamental reason to apply different
> "measuring tapes" to time and space: The constant vacuum speed of light
> can serve as a ruler for both, with the distance of a light second
> equating a second.
>
> It just happens that it's still more practical to use meters for
> space-like dimensions and seconds for time-like dimensions.
When you start measuring "events" which happen at different points in
space and different points in time, it becomes worth using a "spacetime"
measurement which simultaneously encodes both.
(Not that I know much about such things...)
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It seems to me people are confusing mathematical formalisms with reality.
4D Euclidian geometry is an interesting mathematical system. 4D
time-dimension geometry is an interesting mathematical system. 2D Euclid
is an interesting mathematical system. (Euclid was reputedly so
fascinated by it that he was speared to death by some random Roman.)
Whether these systems have any baring on the Real World which we inhabit
is an entirely orthogonal question. ;-)
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clipka wrote:
> Saul Luizaga schrieb:
>
>>>> Or maybe you leave your 3D body and become a 4D spirit that then
>>>> will incarnate a 4D being and so on...
>>>
>>> But if so, how could you possible remember and/or integrate the
>>> experience with a 3D mind? Maybe you could remember that *something*
>>> happened, with a gained benefit of a new spiritual perspective...
>>
>> Is a possibility, but again, who remembers being a 2D person before
>> this life? maybe is part of the "instinct" of each person, but who
>> knows...
>
> You can't be (and never could have been in any prior life) a "2D
> person": Evidently, there /are/ 3 dimensions (or more), so each "2D"
> being must also be embedded in 3D space, and therefore /be/ a 3D being.
You're missing the point: by 2D person we mean you live in a 2D world as
we live in a 3D world, without being able to experience any other
dimension. Of course 2D, 3D, 4D, etc are included in a nD universe but
we're not gonna call everything a nD being or object, we have to call
the object dimensional feature by how many dimensions that being/object
is able to experience not by how many dimension that being/object is
included in.
> Similarly with 4 (space-like) dimensions: Either we /are/ 4D beings, or
> there is no such thing as a 4th dimension.
read above.
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